• 정보보호학회논문지
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• 제26권6호
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• pp.1401-1411
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• 2016

Multi-Prime RSA와 Prime Power RSA는 변형 RSA 시스템의 일종이며, 이 중에서 Multi-Prime RSA는 서로 다른 r(r>2)개의 소수 $p_1,p_2,{\cdots},p_r$에 대하여 $N=p_1p_2{\cdots}p_r$을, Prime Power RSA는 서로 다른 소수 p, q와 양의 정수 r(>1)에 대하여 $N=p^rq$를 각각 모듈러스로 사용한다. 본 논문에서는 Heninger와 Shacham에 의해 제안된 방법을 사용하여 이 시스템들에 대한 안전성을 분석하며 구체적으로, 만약 $p_1,p_2,{\cdots},p_r$의 전체 비트 중 $2-2^{1/r}$의 비율에 해당하는 비트가 랜덤하게 주어지면 $N=p_1p_2{\cdots}p_r$이 다항식 시간 안에 소인수분해될 수 있음을, 그리고 p, q의 전체 비트 중 $2-{\sqrt{2}}$의 비율에 해당하는 비트가 랜덤하게 주어지면 $N=p^rq$가 다항식 시간 안에 소인수분해될 수 있음을 각각 보인다. 또한 $N=p_1p_2p_3$, $N=p^2q$, $N=p^3q$에 적용한 실험 결과를 통해 본 논문의 결과를 검증한다.

• Journal of applied mathematics & informatics
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• 제34권3_4호
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• pp.227-237
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• 2016

In this paper we introduce a new graph labeling called k-prime cordial labeling. Let G be a (p, q) graph and 2 ≤ p ≤ k. Let f : V (G) → {1, 2, . . . , k} be a map. For each edge uv, assign the label gcd (f(u), f(v)). f is called a k-prime cordial labeling of G if |v_f (i) − v_f (j)| ≤ 1, i, j ∈ {1, 2, . . . , k} and |e_f (0) − e_f (1)| ≤ 1 where v_f (x) denotes the number of vertices labeled with x, e_f (1) and e_f (0) respectively denote the number of edges labeled with 1 and not labeled with 1. A graph with a k-prime cordial labeling is called a k-prime cordial graph. In this paper we investigate the k-prime cordial labeling behavior of a star and we have proved that every graph is a subgraph of a k-prime cordial graph. Also we investigate the 3-prime cordial labeling behavior of path, cycle, complete graph, wheel, comb and some more standard graphs.

• 열처리공학회지
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• 제19권5호
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• pp.249-256
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• 2006

Structural studies have been performed on precipitation hardening found in $L1_2$ ordered ${\gamma}^{\prime}-Ni_3(Al,Ti)$ alloys using transmission electron microscopy. A uniform solid solution of ${\gamma}^{\prime}-L1_2$ ordered phase supersaturated with Ni can be obtained by solution annealing in a suitable temperature range. The ${\gamma}^{\prime}$ phase hardens appreciably by the fine precipitation of disordered ${\gamma}$. The shape of ${\gamma}$ precipitates formed during aging is initially spherical or round-cubic and grow into platelets as aging proceeds. High resolution electron microscopy revealed that the ${\gamma}$ precipitates are perfectly coherent with the matrix ${\gamma}^{\prime}$ as long as the ${\gamma}$-precipitates are plates. The loss of coherency initiates by the introduction of dislocations at the ${\gamma}/{\gamma}^{\prime}$ interface followed by the step formation at the dislocations. The ${\gamma}$ precipitates become globular after the loss of coherency. The strength of ${\gamma}^{\prime}-Ni_3(Al,Ti)$ increases over the temperature range of experiment by the precipitation of fine ${\gamma}$ particles. The peak temperature where a maximum strength was obtained shifted to higher temperature.

• Kyungpook Mathematical Journal
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• 제61권1호
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• pp.33-48
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• 2021

Most of the research on weakly prime and weakly 2-absorbing modules is for modules over commutative rings. Only scatterd results about these notions with regard to non-commutative rings are available. The motivation of this paper is to show that many results for the commutative case also hold in the non-commutative case. Let R be a non-commutative ring with identity. We define the notions of a weakly prime and a weakly 2-absorbing submodules of R and show that in the case that R commutative, the definition of a weakly 2-absorbing submodule coincides with the original definition of A. Darani and F. Soheilnia. We give an example to show that in general these two notions are different. The notion of a weakly m-system is introduced and the weakly prime radical is characterized interms of weakly m-systems. Many properties of weakly prime submodules and weakly 2-absorbing submodules are proved which are similar to the results for commutative rings. Amongst these results we show that for a proper submodule Ni of an Ri-module Mi, for i = 1, 2, if N1 × N2 is a weakly 2-absorbing submodule of M1 × M2, then Ni is a weakly 2-absorbing submodule of Mi for i = 1, 2

• 대한수학회보
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• 제55권3호
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• pp.957-965
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• 2018

We study the class $C{\mathcal{V}} ({\Omega})$ of analytic functions f in the unit disk ${\mathbb{D}}=\{z{\in}{\mathbb{C}}$ : ${\mid}z{\mid}$ < 1} of the form $f(z)=z+{\sum}_{n=2}^{\infty}a_nz^n$ satisfying $$1+\frac{zf^{{\prime}{\prime}}(z)}{f^{\prime}(z)}{\in}{\Omega},\;z{\in}{\mathbb{D}}$$, where ${\Omega}$ is a convex and proper subdomain of $\mathbb{C}$ with $1{\in}{\Omega}$. Let ${\phi}_{\Omega}$ be the unique conformal mapping of $\mathbb{D}$ onto ${\Omega}$ with ${\phi}_{\Omega}(0)=1$ and ${\phi}^{\prime}_{\Omega}(0)$ > 0 and $$k_{\Omega}(z)={\displaystyle\smashmargin{2}{\int\nolimits_{0}}^z}{\exp}\({\displaystyle\smashmargin{2}{\int\nolimits_{0}}^t}{\zeta}^{-1}({\phi}_{\Omega}({\zeta})-1)d{\zeta}\)dt$$. Let $z_0,z_1{\in}{\mathbb{D}}$ with $z_0{\neq}z_1$. As the first result in this paper we show that the region of variability $\{{\log}\;f^{\prime}(z_1)-{\log}\;f^{\prime}(z_0)\;:\;f{\in}C{\mathcal{V}}({\Omega})\}$ coincides wth the set $\{{\log}\;k^{\prime}_{\Omega}(z_1z)-{\log}\;k^{\prime}_{\Omega}(z_0z)\;:\;{\mid}z{\mid}{\leq}1\}$. The second result deals with the case when ${\Omega}$ is the right half plane ${\mathbb{H}}=\{{\omega}{\in}{\mathbb{C}}$ : Re ${\omega}$ > 0}. In this case $CV({\Omega})$ is identical with the usual normalized class of convex univalent functions on $\mathbb{D}$. And we derive the sharp upper bound for ${\mid}{\log}\;f^{\prime}(z_1)-{\log}\;f^{\prime}(z_0){\mid}$, $f{\in}C{\mathcal{V}}(\mathbb{H})$. The third result concerns how far two functions in $C{\mathcal{V}}({\Omega})$ are from each other. Furthermore we determine all extremal functions explicitly.

• 대한전기학회논문지
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• 제39권12호
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• pp.1288-1295
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• 1990

In this paper, we propose a parallel processing model for the efficient selection of Prime Implicants of Logic Functions. This model consists of simple parallel processing nodes, connections between them, Max Net (a part of Hamming Net) and quasi essential Prime Implicant selection standard in simplified cost form. Through these, this model selects essential Prime Implicants in a certain period of time regardless of the number of given Prime Implicants and minterms and also selects quasi essential Prime Implicants in short time.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 2011년도 한국컴퓨터종합학술대회논문집 Vol.38 No.1(B)
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• pp.272-275
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• 2011

본 논문에서는 수학에서 사용하는 소수(Prime number)를 찾는 원리에 대한 학습을 위한 게임 기반 학습(Game based learning) 콘텐츠인 Prime Miner라는 게임을 제안한다. Prime Miner는 게임이 가지고 있는 장점과 소수의 원리를 결합하여 게임을 통해 학습자의 흥미를 이끌어 학습에 몰입할 수 있도록 도우며, 학습자가 게임 규칙을 통해 소수의 원리를 합리적으로 배울 수 있도록 유도한다. 본 논문에서는 Prime Miner의 게임 원리와 학습자가 Prime Miner를 통해 소수 학습을 하는 방법을 설명한다. 또한 퍼즐게임에서 종종 발생하는 더 이상 게임을 진행할 수 없는 상태인 교착상태(Deadlock)를 피하기 위한 숫자 타일의 배치에 관한 방법도 제시한다.

• 한국정보처리학회논문지
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• 제7권9호
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• pp.2913-2919
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• 2000

비대칭 암호 알고리즘을 설계하는 데 있어서 매우 큰 소수를 구하는 것은 필수적이다. 그러나 지금까지는 결정론적인(deterministic) 큰 소수를 발견하기는 매우 어려웠기 때문에, 일반적으로 확률적으로 소수일 가능성이 높은 의사소수(psedoprime)를 비대칭 암호 알고리즘에서 사용하였다. 이 논문에서 결정론적인 소수 생성 방법을 제안하며, 제안된 방법에 의해 생성된 소수는 증명이 가능한 100% 정확한 소수이다. 또한 이 방법에 의해 생성된 소수는 신뢰성, 비도, 원시원소(primitive element)생성 능력 등을 보장한다.

• Animal Systematics, Evolution and Diversity
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• 제33권4호
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• pp.274-277
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• 2017

A sea star was collected from the Korea Strait in the waters adjacent to eastern Jeju Island, Korea ($33^{\circ}39^{\prime}86^{{\prime}{\prime}}N$, $127^{\circ}33^{\prime}12^{{\prime}{\prime}}E$) at a depth of 92 m on November 5, 2016. This specimen was identified as Marginaster paucispinus Fisher, 1913, from the family Poraniidae of the order Valvatida, based on morphological characteristics. The genus Marginaster Perrier, 1881 and M. paucispinus, which were first reported in the South China Sea, are new to the Korean fauna. Partial sequences of mitochondrial COI and 16S ribosomal RNA of M. paucispinus were have been determined for the first time and were deposited in GenBank. They are the first molecular records for the genus Marginaster.

• Korean Journal of Mathematics
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• 제17권3호
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• pp.283-291
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• 2009

We investigate the existence of multiple solutions (${\xi},{\eta}$) for perturbations of the parabolic system with Dirichlet boundary condition $$(0.1)\;\begin{array}{lcr}{\xi}_t=-L{\xi}+g_1(3{\xi}+{\eta})-s{\phi}_1-h_1(x,t)\;in\;{\Omega}{\times}(0,\;2{\pi}),\\{\eta}_t=-L{\eta}+g_2(3{\xi}+{\eta})-s{\phi}_1-h_2(x,t)\;in\;{\Omega}{\times}(0,\;2{\pi}).\end{array}$$ We show the existence of multiple solutions (${\xi},{\eta}$) for perturbations of the parabolic system when the nonlinearity $g^{\prime}_1,\;g^{\prime}_2$ are bounded and $3g^{\prime}_1(-{\infty})+g^{\prime}_2(-{\infty})<{\lambda}_1,\;{\lambda}_n<3g^{\prime}_1(+{\infty})+g^{\prime}_2(+{\infty})<{\lambda}_{n+1}$.